#### Solve simultaneous linear equations:

(i) 9 – (x – 4) = y + 7

2 (x + y) = 4 – 3y

(ii) 2x + (x – y)/ 6 = 2

x – (2x + y)/3 = 1.

**Solution:**

(i) 9 – (x – 4) = y + 7

2 (x + y) = 4 – 3y

We can write it as

9 – (x – 4) = y + 7

9 – x + 4 = y + 7

By further calculation

13 – x = y + 7

– x – y = 7 – 13 = – 6

x + y = 6 ….. (1)

2 (x + y) = 4 – 3y

2x + 2y = 4 – 3y

By further calculation

2x + 2y + 3y = 4

So we get

2x + 5y = 4 ….. (2)

Now multiply equation (1) by 5 and (2) by 1

5x + 5y = 30

2x + 5y = 4

By subtracting both the equations

3x = 26

So we get

x = 26/3

Substitute the value of x in (1)

26/3 + y = 6

We can write it as

y = 6 – 26/3

Taking LCM

y = (18 – 26)/3

So we get

y = – 8/3

Therefore, x = 26/3 and y = – 8/3.

(ii) 2x + (x – y)/ 6 = 2

x – (2x + y)/3 = 1

2x + (x – y)/ 6 = 2

Multiply by 6

12x + x – y = 12

By further calculation

13x – y = 12 …… (2)

x – (2x + y)/3 = 1

Multiply by 3

3x – 2x – y = 3

By further calculation

x – y = 3 …… (2)

So we get

x = 3 + y ….. (3)

Substitute the value of x in (1)

13 (3 + y) – y = 12

By further calculation

39 + 13y – y = 12

So we get

12y = 12 – 39 = – 27

By division

y = – 27/12 = – 9/4

Substitute the value of y in (3)

x = 3 + y

x = 3 + (-9)/4

By further calculation

x = 3 – 9/4

Taking LCM

x = (12 – 9)/ 4

x = ¾

Therefore, x = ¾ and y = – 9/4.

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